How To Find The Y Intercept In A Quadratic Equation

Quadratic equations are mathematical functions where one of the x variables is squared, or taken to the second power like this: **x²**. When these functions are graphed, they create a parabola which looks like a curved "U" shape on the graph. This is why a quadratic equation is sometimes called a parabola equation.

Two important values concerning these mathematical functions are the x-intercept and the y-intercept. The x-intercept indicates where the parabola graph of that function crosses the x axis. There can be one or two x intercepts for a single quadratic equations.

The y-intercept indicates where the parabola crosses the y axis. There is only one y intercept for each quadratic equation.

The y-intercept is where the parabola of a function crosses (or intercepts) the y axis. Another way to define the y-intercept is the value of y when x is equal to zero.

Because the y intercept is a point on a graph, you'll usually write it in point/coordinate form. For example, let's say your y value of the y intercept is 6.5. You would write the y intercept as (0, 6.5).

Quadratic equations come in three general forms. These are the standard form, vertex form and factored form.

Standard form looks like this:

**y = ax² + bx + c** where a, b and c are known constants and x and y are variables.

Vertex form looks like this:

**y = a(x + b)² + c** where a, b and c are known constants and x and y are variables.

Factored form looks like this:

**y = a(x + r₁)(x + r₂)** where a is a known constant, r₁ and r₂ are "roots" of the equation (x intercepts), and x and y are variables.

Each of the forms looks drastically different, but the method for finding the y intercept of a quadratic equation is the same despite the various forms.

Standard form is perhaps the most common and the easiest to understand. Simply plug zero (0) in as the value of x in the standard quadratic equation and solve. Here's an example.

Let's say your function is **y = 5x² + 11x + 72**. Assign "0" as your x value and solve.

y = 5(0)² + 11(0) + 72 = 72

You would then write the answer in the coordinate form of (0, 72).

As with standard form, simply plug "0" in as the value of x and solve. Here's an example.

Let's say your function is **y = 134(x + 56)² – 47.** Assign "0" as your x value and solve.

y = 134(0 + 56)² – 47 = 134(0)² – 47 = -47

You would then write the answer in the coordinate form of (0, -47).

Lastly, you have factored form. Again, you simply plug "0" in as the value of x and solve. Here's an example.

Let's say your function is y = 7(x – 8)(x + 2). Assign "0" as your x value and solve.

y = 7(0-8)(0+2) = 7(-8)(2) = -112

You would then write the answer in the coordinate form of (0, -112).

With both standard and vertex form, you may have noticed that the y-intercept value is equal to the value of the c constant in the equation itself. That is going to be true with every parabola/quadratic equation you encounter in those forms.

Simply look for the c constant and that is going to be your y-intercept. You can double check by using the x value of zero method.